How to add more vertices on my object (picture examples)
Apply the subdivision surface modifier. Press Ctrl + A (or use the arrow on the top right) to make the modifier permanent.

Read:
https://blender.stackexchange.com/a/205166/92768
and
How to apply a modifier in V2.9+
But if your &quot;tutorial&quot; doesn't explain those concepts, consider looking at one that explains better. Not all videos are &quot;tutorials&quot;. Some are just not worth your time.